no. 3
Fibration of the phase space for the Korteweg-de Vries equation
Annales de l'Institut Fourier, Tome 41 (1991) no. 3, pp. 539-575.

Dans cet article on démontre que la fibration de L 2 (S 1 ) par des potentiels isospectraux pour l’équation de Schrödinger périodique à une dimension est triviale. Ce résultat peut être appliqué aux solutions de N lacunes de l’équation de Korteweg-de Vries (KDV) sur le cercle : on en déduit que KdV — un système hamiltonien complètement intégrable — a des variables action-angle globales.

In this article we prove that the fibration of L 2 (S 1 ) by potentials which are isospectral for the 1-dimensional periodic Schrödinger equation, is trivial. This result can be applied, in particular, to N-gap solutions of the Korteweg-de Vries equation (KdV) on the circle: one shows that KdV, a completely integrable Hamiltonian system, has global action-angle variables.

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     author = {Kappeler, Thomas},
     title = {Fibration of the phase space for the {Korteweg-de} {Vries} equation},
     journal = {Annales de l'Institut Fourier},
     pages = {539--575},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {41},
     number = {3},
     year = {1991},
     doi = {10.5802/aif.1265},
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     zbl = {0731.58033},
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Kappeler, Thomas. Fibration of the phase space for the Korteweg-de Vries equation. Annales de l'Institut Fourier, Tome 41 (1991) no. 3, pp. 539-575. doi : 10.5802/aif.1265. http://www.numdam.org/articles/10.5802/aif.1265/

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